The check- and/or turn points “Waypoints” listed in the published navigation databases complying with the ARINC-424 standard can be used to define the commonest air routes. For the others, they are often used only to define departure and arrival paths compliant with published approach procedures. Between these prescribed approach paths on departure and/or on arrival, the creation of the air route uses check- and/or turn points “D-Fix” which serve the same purposes as the “Waypoints” with respect to the manual piloting by the intervention of the pilot or with respect to the automatic piloting by the intervention of a flight management computer or an automatic pilot, but the definition of which is the responsibility of the operator. The creation of these check- and/or turn points “D-Fix” presupposes the choice of an air route plot joining, by the shortest path, a departure point to a destination point, taking into account the relief of the region being flown over, regulatory overfly restrictions and lateral maneuvering capabilities of the aircraft having to travel the route, said maneuvering capabilities being dependent on the aircraft and its flight configuration. Often, the choice of the plot of the air route must comply with a vertical flight and speed profile that is prescribed, either by circumstances, or by the desire to minimize the cost of the mission, for example by searching for a minimum fuel consumption.
There is a large body of literature on how to determine the horizontal profile of the air route that an aircraft must follow to fulfill the objectives of a mission for the lowest cost, the cost being assessed in terms of local constraints, taking into consideration the speed of the aircraft, the maximum acceptable lateral acceleration, the risks of collisions with the relief, enemy threats in the case of a military mission, deviations relative to a direct path and the extra length traveled compared to the shortest path. The literature mainly contains methods consisting in subdividing the region being flown over into individual cells by means of a geographic locating grid, choosing a sequence of individual cells to be followed to go, at the lowest cost, from the departure point to the destination point, and placing along the sequence of chosen individual cells check- and/or turn points “D-Fix” compatible with a flyable path. Among these methods, there are so-called grid-based methods, one example of which is described in the American patent U.S. Pat. No. 4,812,990, which implement a search for a minimum cost path out of all the possible paths linking the departure point to the destination point via the centers of the cells of the grid, so-called graph-based methods, one example of which is described in the American patent U.S. Pat. No. 6,266,610, which implement a search for a minimum cost path out of all the paths linking the departure point to the destination point via the sides or the diagonals of the cells and hybrid grid- and graph-based methods such as that described in the American patent U.S. Pat. No. 6,259,988.
All these methods come up against the difficulty of finding a sequence of individual cells resulting in a minimum cost path, caused by the large number of possible sequences, a number that increases exponentially when the pitch of the geographic location grid is tightened. Most of them propose progressive, step-by-step plotting methods that seek to limit as quickly as possible the search field out of all of the possible sequences, but they always demand very significant computation power, which is often not available on board an aircraft. Furthermore, they take little or no account of the comfort imperatives of civilian transport aircraft which require the frequency and rapidity of changes of heading or altitude to be minimized.
In fact, the problem of determining the horizontal profile of an air route lies in determining a curvilinear path that is direct and therefore of minimum length, circumnavigating the reliefs that cannot be crossed with the prescribed vertical flight and speed profile. This determination of a direct curvilinear path is based on estimations of curvilinear distances in the presence of static constraints (obstacles to be circumnavigated) and dynamic constraints (vertical flight and speed profile). Now, such estimations can be made with a lower computation cost, in the way described in the French patent application FR 2.860.292, by means of propagation distance transforms, also called chamfer distance transforms, which make do with computations on integer numbers.
The applicant has already proposed, in the French patent applications FR 2.864.312 and FR 2.868.835, the implementation of propagation distance transforms to create curvilinear distance maps in the context of a display of electronic aeronautical navigation maps showing the reliefs to be circumnavigated in the region being flown over and the lateral safety margins to be observed, and in the context of aircraft guidance toward a safe zone, with no maneuvering constraint in the horizontal plane, notably to negate an established risk of collision with the ground.